find the "overlap" between 2 python lists

Question

Given 2 lists:

a = [3,4,5,5,5,6]
b = [1,3,4,4,5,5,6,7]

I want to find the "overlap":

c = [3,4,5,5,6]

I'd also like it if i could extract the "remainder" the part of a and b that's not in c.

a_remainder = [5,]
b_remainder = [1,4,7,]

Note: a has three 5's in it and b has two. b has two 4's in it and a has one.

The resultant list c should have two 5's (limited by list b) and one 4 (limited by list a).

This gives me what i want, but I can't help but think there's a much better way.

import copy

a = [3,4,5,5,5,6]
b = [1,3,4,4,5,5,6,7]

c = []
for elem in copy.deepcopy(a):
    if elem in b:
        a.pop(a.index(elem))
        c.append(b.pop(b.index(elem)))

# now a and b both contain the "remainders" and c contains the "overlap"

On another note, what is a more accurate name for what I'm asking for than "overlap" and "remainder"?

Answer 1

collection.Counter available in Python 2.7 can be used to implement multisets that do exactly what you want.

a = [3,4,5,5,5,6]
b = [1,3,4,4,5,5,6,7]

a_multiset = collections.Counter(a)
b_multiset = collections.Counter(b)

overlap = list((a_multiset & b_multiset).elements())
a_remainder = list((a_multiset - b_multiset).elements())
b_remainder = list((b_multiset - a_multiset).elements())

print overlap, a_remainder, b_remainder

Answer 2

Use python set

intersection = set(a) & set(b)
a_remainder = set(a) - set(b)
b_remainder = set(b) - set(a)